An operadic approach to deformation quantization of compatible Poisson brackets

Details An operadic approach to deformation quantization of compatible Poisson brackets An operadic approach to deformation quantization of compatible Poisson brackets

2006-11-06

arxiv.org/abs/math/0611154v4

J. Gen. Lie Theory and Appl., 1 (2007), No. 2, 107-115

Mathematics

Quantum Algebra

11 pages, no figures, typos corrected

Scientific paper

We construct an analogue of the Livernet--Loday operad for two compatible
brackets. The Livernet--Loday operad can be used to define $\star$-products and
deformation quantization for Poisson structures. We make use of our operad in
the same way, introducing a definition of (operadic) deformation quantization
of compatible Poisson structures.

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